FRM Exam Part I · Commodity Forwards and Futures

Hedging with Commodity Futures and Basis Risk

Updated 11 October 2026 · Fact-checked

A commodity hedge takes a futures position opposite to your physical exposure: producers go short, consumers go long. The hedge locks in the futures price only if the basis (spot minus futures) is known at close-out. Basis risk is the uncertainty in that basis. Effective price = initial futures price + final basis.

Understand Hedging with Commodity Futures and Basis Risk

Commodity prices move a lot. A farmer, an oil producer, an airline and a food manufacturer all face price risk on something they will buy or sell later. A futures contract lets them fix a price today for delivery later, without waiting for the physical trade.

A short hedge is used by someone who owns or will produce the commodity. You sell futures now. If the price falls, the loss on the physical sale is offset by the gain on the futures. A long hedge is used by someone who will need to buy the commodity. You buy futures now. If the price rises, the extra cost is offset by the futures gain.

The hedge is rarely perfect. The basis is the spot price minus the futures price (the convention used here; some texts reverse it, so check the question). If the asset hedged is exactly the asset underlying the futures and the hedge ends in the delivery month, the basis is close to zero at expiry. In practice, you often close out before delivery, or your grade, location or timing differs from the contract. Then the basis at close-out is unknown. That uncertainty is basis risk.

Basis risk has three common sources. Maturity mismatch: no contract expires exactly when you need the hedge to end, so you pick a later month and close out early. Grade or location mismatch: you hedge jet fuel with heating oil futures, or a local grain grade with a benchmark contract. This is a cross hedge. Rolling: a long-dated exposure is hedged with a short-dated contract that is rolled forward, adding the risk that the spread between contract months changes.

A hedger swaps price risk for basis risk. This is usually a good trade because basis moves less than the outright price. A strengthening basis (spot rises relative to futures) helps a short hedger. A weakening basis helps a long hedger. In cross hedges you also choose how many contracts to use, with the minimum variance hedge ratio.

Key formulas to remember

Basis: b = S − F; Spot minus futures at the same date. b1 is the basis when you open the hedge, b2 when you close it. Check the question's sign convention.
Effective price, short hedge: Price received = S2 + (F1 − F2) = F1 + b2; You sell the physical at S2 and gain F1 − F2 on the short futures. Only b2 is uncertain.
Effective cost, long hedge: Price paid = S2 − (F2 − F1) = F1 + b2; You buy the physical at S2 and gain F2 − F1 on the long futures. Same expression as the short hedge.
Minimum variance hedge ratio: h* = ρ × σS ÷ σF; ρ is the correlation between changes in spot and futures prices. σS and σF are the standard deviations of those changes over the hedge life.
Number of contracts: N* = h* × QA ÷ QF; QA is the exposure size, QF is the size of one futures contract. Round to the nearest whole contract.
Hedge effectiveness: R² = ρ²; The proportion of the variance of the spot price change removed by the optimal hedge.
Basis effect on a hedge: Strengthening basis helps shorts; weakening basis helps longs; Holds when basis is defined as spot minus futures.

How to solve Hedging with Commodity Futures and Basis Risk questions

Use this order for any hedging or basis question. It keeps the signs straight and separates the hedge direction from the basis effect.

1Identify the exposure. Will you sell the commodity (short hedge) or buy it (long hedge)?
2Write down the futures position that offsets it: short futures for a seller, long futures for a buyer.
3Note the contract size and decide the number of contracts. If the asset differs from the contract, compute h* = ρ × σS ÷ σF and N* = h* × QA ÷ QF.
4Record F1 (futures price when the hedge starts), and S2 and F2 (prices when it ends).
5Compute the basis at close-out, b2 = S2 − F2, and compare it with b1 if given. State whether the basis strengthened or weakened.
6Compute the effective price: F1 + b2. Cross-check by adding the physical result and the futures gain or loss.
7Multiply by the quantity if a total is asked, and round contracts only at the end.
8State what risk remains: basis risk, plus any hedge ratio or rolling risk.

Quickest way: Effective price shortcut: F1 + b2

When to use it: Any question that gives the opening futures price and the closing spot and futures prices, and asks for the net price received or paid.

Take the opening futures price F1.
Compute b2 = S2 − F2 at close-out.
Add them: F1 + b2. This works for both short and long hedges.
For contract counts, compute ρ × σS ÷ σF first, then multiply by exposure ÷ contract size.
Eliminate options that equal S2 (unhedged) or F1 (ignores basis), and options that flip the basis sign.

Common mistakes in Hedging with Commodity Futures and Basis Risk

Assuming a futures hedge fixes the price exactly at F1.
Textbook intros say the hedge locks in the futures price.
Fix: It locks in F1 only if b2 = 0. Otherwise the result is F1 + b2, so basis risk remains.
Getting the sign of the basis effect wrong.
Mixing up which direction helps a seller and which helps a buyer, or using a different basis definition.
Fix: With basis = spot − futures, a short hedger gains when it strengthens and a long hedger gains when it weakens. Use F1 + b2 and let the numbers decide.
Using a hedge ratio of 1 in a cross hedge.
One contract per unit of exposure feels natural.
Fix: Use h* = ρ × σS ÷ σF. A hedge ratio of 1 is optimal only when σS = σF and ρ = 1.
Swapping σS and σF in the hedge ratio.
Both are standard deviations, and the order is easy to forget.
Fix: Spot volatility goes on top, futures volatility below. The ratio is the slope of spot changes regressed on futures changes.
Rounding the hedge ratio or contract number too early.
Wanting tidy intermediate numbers.
Fix: Carry full precision and round only the final number of contracts to the nearest whole number.
Calling the hedge risk-free.
Confusing removing price risk with removing all risk.
Fix: Name the remaining risks: basis risk, imperfect correlation, rolling risk and margin cash-flow (funding) risk.

Worked examples

Example 1

An airline expects to buy 2,000,000 gallons of jet fuel in three months. It hedges with heating oil futures, each contract covering 42,000 gallons. Over the hedge period the standard deviation of jet fuel price changes is 0.032 and of futures price changes is 0.040. The correlation is 0.75. How many futures contracts should the airline buy? (A) 24 (B) 29 (C) 48 (D) 67

Show the solution

The airline will buy fuel, so this is a long hedge: buy futures.
Hedge ratio: h* = ρ × σS ÷ σF = 0.75 × 0.032 ÷ 0.040 = 0.024 ÷ 0.040 = 0.60.
Contracts: N* = h* × QA ÷ QF = 0.60 × 2,000,000 ÷ 42,000 = 1,200,000 ÷ 42,000 = 28.57.
Round to the nearest whole contract: 29.
Check: a hedge ratio of 1 would give 47.6 contracts (about 48), which over-hedges because the correlation is below 1.

Answer: (B) 29 long futures contracts. The remaining risk is basis risk from using heating oil to hedge jet fuel.

Example 2

A corn farmer expects to sell 50,000 bushels in December. In the summer she sells 10 December corn futures contracts (5,000 bushels each) at $4.60 per bushel. At that time spot is $4.40. In December she sells the corn at spot of $4.30 and closes the futures at $4.45. What net price per bushel does she effectively receive? (A) $4.30 (B) $4.45 (C) $4.60 (D) $4.75

Show the solution

She owns the corn, so this is a short hedge: F1 = $4.60.
Opening basis b1 = 4.40 − 4.60 = −0.20.
Closing basis b2 = S2 − F2 = 4.30 − 4.45 = −0.15. The basis strengthened, which helps a short hedger.
Effective price = F1 + b2 = 4.60 + (−0.15) = $4.45.
Cross-check: physical sale $4.30 plus futures gain (4.60 − 4.45) = 0.15 gives $4.45.
Total proceeds = 50,000 × 4.45 = $222,500.

Answer: (B) $4.45 per bushel, or $222,500 in total. Option (C) ignores the basis, and option (D) adds the basis change with the wrong sign.

Exam tips

Look for the words producer, farmer, miner (short hedge) and refiner, airline, manufacturer (long hedge) to fix direction quickly.
Always check how basis is defined in the question. If the sign convention is reversed, the strengthening and weakening results reverse too.
Expect cross-hedge questions that give ρ, σS and σF. Compute h* first, then contracts, and watch the contract size.
Wrong options usually equal the unhedged price S2, the initial futures price F1, or the answer with the basis sign flipped. Compute F1 + b2 and compare.
Conceptual questions often ask what risk remains after hedging. The best answer is basis risk, not price risk.

Practice questions from Commodity Forwards and Futures

Hedging with Commodity Futures and Basis Risk in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Hedging with Commodity Futures and Basis Risk: frequently asked questions

What is basis risk in commodity hedging?

It is the risk that the difference between spot and futures prices changes between opening and closing the hedge. It arises from timing, grade or location mismatch, and from closing out before delivery. The hedger's final price is F1 plus the closing basis.

What is the difference between a short hedge and a long hedge?

A short hedge sells futures to protect against falling prices on a commodity you own or will produce. A long hedge buys futures to protect against rising prices on a commodity you will need to buy. Both lock in F1 plus the closing basis.

Does a perfect hedge exist with commodity futures?

Only if the hedged asset matches the contract and the hedge ends at delivery, so the basis at close-out is known. In most real cases some basis risk remains. Margin calls can also create funding risk.

How do I compute the number of futures contracts for a cross hedge?

Compute h* = ρ × σS ÷ σF, then N* = h* × exposure size ÷ contract size. Round to the nearest whole number of contracts. The hedge ratio is below 1 when ρ is low or the futures are more volatile than the spot.